Journal articles on the topic 'Plates (Engineering) – Vibration ; Structural dynamics – Mathematical models'
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1
Borkovic, Aleksandar, Dragan Milasinovic, Valentina Golubovic-Bugarski, Ognjen Mijatovic, and Manuel Desancic. "Experimental and numerical identification of structural modes for engineering education." Facta universitatis - series: Architecture and Civil Engineering 12, no. 2 (2014): 161–72. http://dx.doi.org/10.2298/fuace1402161b.
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Development of simple classroom demonstration device and software for visualization of structural normal modes is presented. Device is made of parts of old speaker, controlled with personal computer, where the harmonic motion of solenoid is used as an excitation for beam and plate models. Simple code for finite element free vibration analysis of plates is written in Wolfram Mathematica. Good agreement of results and attractive visual patterns of normal modes attracted attention of students. Results are confirmed using modern modal testing methods. Presented approach is complementary to standard teaching of structural dynamics.
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Tian, Ali, Renchuan Ye, Peng Ren, Pengming Jiang, Zengtao Chen, Xiaochun Yin, and Yuanshuai Zhao. "New Higher-Order Models for Sandwich Plates with a Flexible Core and their Accuracy Assessment." International Journal of Structural Stability and Dynamics 19, no. 03 (March 2019): 1950024. http://dx.doi.org/10.1142/s021945541950024x.
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Two higher-order analytical models based on a new higher-order theory for sandwich plates with flexible cores are developed considering the effect of the core material density and skin-to-core-stiffness-ratio (SCSR). The main difference between the two models is the role of the flexible core in the dynamic response of sandwich plates with cores of different stiffnesses. Firstly, the governing equations of a simply supported sandwich plate with a flexible core are derived based on the two models, and the analytical solutions are determined by using Navier’s approach. Then, the free vibration, static, dynamic bending and stress field characteristics of the sandwich plates with different SCSRs are investigated. The results obtained by the proposed method are compared with other published results. In particular, an accuracy assessment of the present dynamic models is conducted for different SCSRs. Finally, conclusions on the applicability of the proposed method and other theories on sandwich plates with different SCSRs are drawn.
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Zhang, Yichi, and Bingen Yang. "Medium-Frequency Vibration Analysis of Timoshenko Beam Structures." International Journal of Structural Stability and Dynamics 20, no. 13 (September 22, 2020): 2041009. http://dx.doi.org/10.1142/s0219455420410096.
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Medium-frequency (mid-frequency) vibration analysis of complex structures plays an important role in automotive, aerospace, mechanical, and civil engineering. Flexible beam structures modeled by the classical Euler–Bernoulli beam theory have been widely used in various engineering problems. A kinematic hypothesis made in the Euler–Bernoulli beam theory is that the plane sections of a beam normal to its neutral axis remain planes after the beam experiences bending deformation, which neglects shear deformation. However, previous investigations found out that the shear deformation of a beam (even with a large slenderness ratio) becomes noticeable in high-frequency vibrations. The Timoshenko beam theory, which describes both bending deformation and shear deformation, would naturally be more suitable for medium-frequency vibration analysis. Nevertheless, vibrations of Timoshenko beam structures in a medium frequency region have not been well studied in the literature. This paper presents a new method for mid-frequency vibration analysis of two-dimensional Timoshenko beam structures. The proposed method, which is called the augmented Distributed Transfer Function Method (DTFM), models a Timoshenko beam structure by a spatial state-space formulation in the [Formula: see text]-domain. The augmented DTFM determines the frequency response of a beam structure in an exact and analytical form, in any frequency region covering low, middle, or high frequencies. Meanwhile, the proposed method provides the local information of a beam structure, such as displacement, shear deformation, bending moment and shear force at any location, which otherwise would be very difficult with energy-based methods. The medium-frequency analysis by the augmented DTFM is validated in numerical examples, where the efficiency and accuracy of the proposed method is demonstrated. Also, the effects of shear deformation on the dynamic behaviors of a beam structure at medium frequencies are examined through comparison of the Timoshenko beam and Euler–Bernoulli beam theories.
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Wu, D., and S. S. Law. "Crack Identification in Thin Plates With Anisotropic Damage Model and Vibration Measurements." Journal of Applied Mechanics 72, no. 6 (February 7, 2005): 852–61. http://dx.doi.org/10.1115/1.1985432.
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Many approaches on modeling of cracks in structural members have been reported in the literatures. However, most of them are explicitly developed for the purpose of studying the changes in static and dynamic responses of the structure due to the crack damage, which is a forward problem mathematically. Thereby the use of these models is inconvenient or even impossible for detecting damage in structures from vibration measurements, which is usually an inverse problem. An anisotropic damage model is proposed for a two-dimensional plate element with an edge-parallel crack. The cracked plate element is represented by a plate element with orthotropic anisotropic material expressed in terms of the virgin material stiffness and a tensor of damage variables. Instead of using the effective stress concept, strain equivalence, or strain energy equivalence principles, the vector of damage variables is identified based on the principle of equivalent static and dynamic behaviors. A nonmodel-based damage identification approach is developed incorporating the proposed anisotropic model and the estimated uniform load surface curvature (ULSC) from vibration measurements. The actual length of the crack is then predicted from the identified variables based on conservation law of potential energy for crack growth. The validity of the methodology is demonstrated by numerical examples and experiment results with comparison to results from existing strain energy equivalence theory.
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Xiao, Tian Yin, Jian Gang Han, and Hong Bo Gao. "Finite Element Model Updating of Space Grid Structures." Advanced Materials Research 243-249 (May 2011): 116–19. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.116.
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The aim of updating models is to generate improved numerical models which may be applied in order to predict actual dynamic behaviors of the structure. The approach of numerical predictions to the behavior of a physical system is limited by the assumptions used in the development of the mathematical model. Model updating is about correcting invalid assumptions by processing vibration test results. Updating by improving the physical meaning of the model requires the application of considerable physical insight in the choice of parameters to update and the arrangement of constraints, force inputs and response measurements in the vibration test. The choice of updating parameters is the most important and the numerical predictions should be sensitive to small changes in the parameters. So methods used in model updating places a demand that the mass, stiffness and damping terms should be based on physically meaningful parameters. Using the structure frequency and local modal shape acquired from structural time-history responses, a model updating method of space grid structures was established in this paper. A numerical example is provided to prove the accuracy of this method. The results show that the method can be effectively used to correct the finite element model of space grid structures.
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Hache, F., N. Challamel, and I. Elishakoff. "Nonlocal Approaches for the Vibration of Lattice Plates Including Both Shear and Bending Interactions." International Journal of Structural Stability and Dynamics 18, no. 07 (July 2018): 1850094. http://dx.doi.org/10.1142/s0219455418500943.
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The present study investigates the dynamical behavior of lattice plates, including both bending and shear interactions. The exact natural frequencies of this lattice plate are calculated for simply supported boundary conditions. These exact solutions are compared with some continuous nonlocal plate solutions that account for some scale effects due to the lattice spacing. Two continualized and one phenomenological nonlocal UflyandMindlin plate models that take into account both the rotary inertia and the shear effects are developed for capturing the small length scale effect of microstructured (or lattice) thick plates by associating the small length scale coefficient introduced in the nonlocal approach to some length scale coefficients given in a Taylor or a rational series expansion. The nonlocal phenomenological model constitutes the stress gradient Eringen’s model applied at the plate scale. The continualization process constructs continuous equation from the one of the discrete lattice models. The governing partial differential equations are solved in displacement for each nonlocal plate model. An exact analytical vibration solution is obtained for the natural frequencies of the simply supported rectangular nonlocal plate. As expected, it is found that the continualized models lead to a constant small length scale coefficient, whereas for the phenomenological nonlocal approaches, the coefficient, calibrated with respect to the element size of the microstructured plate, is structure-dependent. Moreover, comparing the natural frequencies of the continuous models with the exact discrete one, it is concluded that the continualized models provide much more accurate results than the nonlocal Uflyand–Mindlin plate models.
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Moon, Francis C., and Preston D. Stiefel. "Coexisting chaotic and periodic dynamics in clock escapements." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, no. 1846 (July 28, 2006): 2539–64. http://dx.doi.org/10.1098/rsta.2006.1839.
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This paper addresses the nature of noise in machines. As a concrete example, we examine the dynamics of clock escapements from experimental, historical and analytical points of view. Experiments on two escapement mechanisms from the Reuleaux kinematic collection at Cornell University are used to illustrate chaotic-like noise in clocks. These vibrations coexist with the periodic dynamics of the balance wheel or pendulum. A mathematical model is presented that shows how self-generated chaos in clocks can break the dry friction in the gear train. This model is shown to exhibit a strange attractor in the structural vibration of the clock. The internal feedback between the oscillator and the escapement structure is similar to anti-control of chaos models.
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Gozum, Mehmet Murat, Amirreza Aghakhani, Gokhan Serhat, and Ipek Basdogan. "Electroelastic modeling of thin-laminated composite plates with surface-bonded piezo-patches using Rayleigh–Ritz method." Journal of Intelligent Material Systems and Structures 29, no. 10 (March 1, 2018): 2192–205. http://dx.doi.org/10.1177/1045389x18758189.
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Laminated composite panels are extensively used in various engineering applications. Piezoelectric transducers can be integrated into such composite structures for a variety of vibration control and energy harvesting applications. Analyzing the structural dynamics of such electromechanical systems requires precise modeling tools which properly consider the coupling between the piezoelectric elements and the laminates. Although previous analytical models in the literature cover vibration analysis of laminated composite plates with fully covered piezoelectric layers, they do not provide a formulation for modeling the piezoelectric patches that partially cover the plate surface. In this study, a methodology for vibration analysis of laminated composite plates with surface-bonded piezo-patches is developed. Rayleigh–Ritz method is used for solving the modal analysis and obtaining the frequency response functions. The developed model includes mass and stiffness contribution of the piezo-patches as well as the two-way electromechanical coupling effect. Moreover, an accelerated method is developed for reducing the computation time of the modal analysis solution. For validations, system-level finite element simulations are performed in ANSYS software. The results show that the developed analytical model can be utilized for accurate and efficient analysis and design of laminated composite plates with surface-bonded piezo-patches.
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Yao, Qiang, Xingguo Yang, and Hongtao Li. "A Fuzzy AHP-Based Method for Comprehensive Blasting Vibration Comfort Evaluation Forecast." Advances in Civil Engineering 2020 (February 8, 2020): 1–11. http://dx.doi.org/10.1155/2020/8919314.
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Blasting vibration comfort evaluation (BVCE) is an emerging interdisciplinary multilayer and multifactor issue that involves explosion mechanics, structural dynamics, biodynamics, statistics, psychology, and many other disciplines. The evaluation index system of blasting vibration comfort is divided into three levels: target level, criterion level, and index level. The absorption blasting vibration energy (ABVE) value is calculated based on triangular membership function, while the value of residual subjective evaluation index is obtained based on evaluation standard. The weight of each index is determined using the analytic hierarchy process. By developing the mathematical models, defining and quantifying the BVCE indices, and analyzing the factors that influence blasting vibration comfort in a hierarchical manner, this study proposes an exploratory fuzzy AHP-based method for comprehensive BVCE. The feasibility\reliability of this method is verified on the basis of 166 groups of comfort survey data. It is found that more than 85% and 62% of forecast results had an error of less than 1.0 and 0.5, respectively. The aim of combining qualitative and quantitative approaches to evaluate and forecast blasting vibration comfort can be initially realized. Further sensitivity analyses show that the absorbed blasting vibration energy (ABVE) index had the most significant influence, followed by environmental vibration, environmental noise, blasting noise, and lastly other factors on blasting vibration comfort. The presented results can provide a reference and guidance for actively creating the favorable conditions in blasting construction practice to improve the resident comfort and to realize the goal of “undisturbing, safe, and harmonious blasting construction.”
10
Liu, Qi, Yong Xu, Jürgen Kurths, and Xiaochuan Liu. "Complex nonlinear dynamics and vibration suppression of conceptual airfoil models: A state-of-the-art overview." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 6 (June 2022): 062101. http://dx.doi.org/10.1063/5.0093478.
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During the past few decades, several significant progresses have been made in exploring complex nonlinear dynamics and vibration suppression of conceptual aeroelastic airfoil models. Additionally, some new challenges have arisen. To the best of the author’s knowledge, most studies are concerned with the deterministic case; however, the effects of stochasticity encountered in practical flight environments on the nonlinear dynamical behaviors of the airfoil systems are neglected. Crucially, coupling interaction of the structure nonlinearities and uncertainty fluctuations can lead to some difficulties on the airfoil models, including accurate modeling, response solving, and vibration suppression. At the same time, most of the existing studies depend mainly on a mathematical model established by physical mechanisms. Unfortunately, it is challenging and even impossible to obtain an accurate physical model of the complex wing structure in engineering practice. The emergence of data science and machine learning provides new opportunities for understanding the aeroelastic airfoil systems from the data-driven point of view, such as data-driven modeling, prediction, and control from the recorded data. Nevertheless, relevant data-driven problems of the aeroelastic airfoil systems are not addressed well up to now. This survey contributes to conducting a comprehensive overview of recent developments toward understanding complex dynamical behaviors and vibration suppression, especially for stochastic dynamics, early warning, and data-driven problems, of the conceptual two-dimensional airfoil models with different structural nonlinearities. The results on the airfoil models are summarized and discussed. Besides, several potential development directions that are worth further exploration are also highlighted.
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Jiang, Mian, Yingwei Kuang, Jigang Wu, and Xuejun Li. "Rub-Impact Detection in Rotor Systems with Pedestal Looseness Using a Nonlinearity Evaluation." Shock and Vibration 2018 (November 27, 2018): 1–15. http://dx.doi.org/10.1155/2018/7928164.
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In this paper, a nonlinearity evaluation is proposed in order to identify the rub-impact in rotor systems with pedestal looseness. Nonlinear mathematical models have been established for bearing-rotor systems with single pedestal looseness and pedestal looseness coupled with rub-impact. Piecewise linear stiffness and damping are considered regarding the position of pedestal looseness, while radial impact forces are defined using the Colulomb type of frictional relationship during rub-impact. The nonlinearity evaluation is employed to quantify the nonlinearity of the dynamics of bearing-rotor systems, which are calculated at different looseness clearances. The experiments for rotor systems with pure pedestal looseness and pedestal looseness coupled with rub-impact are conducted respectively to collect the vibration signals on different looseness clearances. Two different curves are obtained using the nonlinear fitting method for the values of nonlinearity evaluation. The rub-impact within rotor systems with pedestal looseness can then be identified by comparing the curves that denote the trend of nonlinearity evaluation for the measured vibration responses.
12
Xin, Yunsheng, Gening Xu, and Nina Su. "Dynamic Optimization Design of Cranes Based on Human–Crane–Rail System Dynamics and Annoyance Rate." Shock and Vibration 2017 (2017): 1–19. http://dx.doi.org/10.1155/2017/8376058.
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The operators of overhead traveling cranes experience discomfort as a result of the vibrations of crane structures. These vibrations are produced by defects in the rails on which the cranes move. To improve the comfort of operators, a nine-degree-of-freedom (nine-DOF) mathematical model of a “human–crane–rail” system was constructed. Based on the theoretical guidance provided in ISO 2631-1, an annoyance rate model was established, and quantization results were determined. A dynamic optimization design method for overhead traveling cranes is proposed. A particle swarm optimization (PSO) algorithm was used to optimize the crane structural design, with the structure parameters as the basic variables, the annoyance rate model as the objective function, and the acceleration amplitude and displacement amplitude of the crane as the constraint conditions. The proposed model and method were used to optimize the design of a double-girder 100 t–28.5 m casting crane, and the optimal parameters are obtained. The results show that optimization decreases the human annoyance rate from 28.3% to 9.8% and the root mean square of the weighted acceleration of human vibration from 0.59 m/s2to 0.38 m/s2. These results demonstrate the effectiveness and practical applicability of the models and method proposed in this paper.
13
Zarraga, Ondiz, Imanol Sarría, Jon García-Barruetabeña, and Fernando Cortés. "An Analysis of the Dynamical Behaviour of Systems with Fractional Damping for Mechanical Engineering Applications." Symmetry 11, no. 12 (December 11, 2019): 1499. http://dx.doi.org/10.3390/sym11121499.
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Fractional derivative models are widely used to easily characterise more complex damping behaviour than the viscous one, although the underlying properties are not trivial. Several studies about the mathematical properties can be found, but are usually far from the most daily applications. Thus, this paper studies the properties of structural systems whose damping is represented by a fractional model from the point of view of a mechanical engineer. First, a single-degree-of-freedom system with fractional damping is analysed. Specifically, the distribution of the poles and the dynamic response to several excitations is studied for different model parameter values highlighting dissimilarities from systems with conventional viscous damping. In fact, thanks to fractional models, particular behaviours are observed that cannot be reproduced by classical ones. Finally, the dynamics of a machine shaft supported by two bearings presenting fractional damping is analysed. The study is carried out by the Finite Element method, deriving in a system with symmetric matrices. Eigenvalues and eigenvectors are obtained by means of an iterative method, and the effect of damping is visualised on the mode shapes. In addition, the response to a perturbation is computed, revealing the influence of the model parameters on the resulting vibration.
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Filomeno Amador, Luis Daniel, and Eduardo Castillo Castañeda. "Kinematic and dynamic analysis of an omnidirectional mobile platform driven by a spherical wheel." Mechanical Sciences 13, no. 1 (February 7, 2022): 31–39. http://dx.doi.org/10.5194/ms-13-31-2022.
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Abstract. The increased use of spherical wheels has allowed mobile robots to have a higher degree of maneuverability, less complex path planning and less complex control schemes. The geometry and design of the mobile robot are the principal attributes that guarantee an omnidirectional motion. Furthermore, the platform uses an active spherical wheel and four passive spherical wheels to get the best stability when the robot uses a terminal element (Kärcher). The proposed model has been designed to improve the omnidirectional motion issues, such as vibration into the platform or lack of punctual contact between the wheel and the floor, compared to mobile robots using Mecanum wheels and more than one active wheel; due to the design concept, all the mathematical formulations, kinematics and dynamics presents how the models are validated with computer simulations.
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Liu, Hongtuo, Fangwei Xie, Kai Zhang, Xinxing Zhang, Jin Zhang, Cuntang Wang, and Hao Li. "Effect of air chamber and oil properties on damping characteristics of single-tube pneumatic shock absorber." International Journal of Structural Integrity 9, no. 1 (February 5, 2018): 27–37. http://dx.doi.org/10.1108/ijsi-03-2017-0017.
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Purpose The shock absorber is an important component of vehicle suspension that attenuates the vehicle vibration. Its running state directly affects the performance of the vehicle suspension. The purpose of this paper is to quantitatively study the relationship between damping characteristics and air chamber and oil properties in single-tube pneumatic shock absorber. Design/methodology/approach Combined with the principle of fluid dynamics and hydraulic transmission technology, the rebound stroke and compression stroke mathematical models, and damping characteristics simulation model are established to investigate the effect of the air chamber and oil property on damping characteristics. Findings Research results show that the initial pressure of the air chamber is the key parameter which influences the damping characteristics of the shock absorber. The change of the initial pressure has more impact on damping force, and less impact on the speed characteristic; the initial volume of the air chamber almost has no effect on the damping characteristics. The density and viscosity of the oil have certain influence on the damping characteristics. Therefore, selecting suitable damping oil is very important. Originality/value Using Matlab/Simulink software to build simulation models, its results are very accurate. The conclusions can provide a theoretical reference for the structure design of a single-tube pneumatic shock absorber.
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Meng, Dejian, Lijun Zhang, Xiaotian Xu, Yousef Sardahi, and Gang S. Chen. "Sensing and Quantifying a New Mechanism for Vehicle Brake Creep Groan." Shock and Vibration 2019 (February 26, 2019): 1–10. http://dx.doi.org/10.1155/2019/1843205.
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This paper investigates the creep groan of a vehicle’s brake experimentally, analytically, and numerically. Experimentally, the effects of acceleration on caliper and strut, noise, brake pressure, and tension are measured. The results show that the measured signals and their relevant spectra broadly capture the complex vibrations of creep groan. This includes the simple stick-slip, severe stick-slip vibrations/resonances, multiple harmonics, half-order harmonics; stick-slip-induced impulsive vibrations, steady/unstable vibrations, and their transitions. Analytically, a new mathematical model is presented to capture the unique features of half-order harmonics and the connections to fundamental stick-slip/resonant frequency and multiple harmonics. The analytical solution and the experimental results show that the vibro-impact of the brake pad-disc system can be triggered by severe stick-slip vibrations and is associated with instable, impulsive stick-slip vibration with wideband. The induced stick-slip vibro-impact can evolve into a steady and strong state with half-order, stick-slip fundamental, and multiple-order components. This new mechanism is different from all previously proposed mechanisms of creep groan in that we also view some type of creep groan as a stick-slip vibration-induced vibro-impact phenomenon in addition to conventional stick-slip phenomena. The new mechanism comprehensively explains the complex experimental phenomena reported in the literature. Numerically, the salient features of phase diagrams of instable stick-slip and vibro-impact are examined by using a seven-degree-of-freedom brake system model, which shows that the phase diagrams of the dynamics of creep groan with and without vibro-impact are substantially different. The phase diagram of the dynamics with vibro-impact is closer to the experimental results. In contrast to existing mechanisms, the proposed new mechanism encompasses the instable stick-slip nature of creep groan and elaborates the inherent connections and transition of the spectrogram. The new knowledge can be used to attain critical improvements to brake noise and vibration analysis and design. By applying the proposed new model in addition to existing models, all experimental phenomena in creep groan are elaborated and quantified.
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Mohan, Sankar K., and Bandaru V. Ramarao. "A Comprehensive Study of Self-Induced Torque Amplification in Rotary Viscous Couplings." Journal of Tribology 125, no. 1 (December 31, 2002): 110–20. http://dx.doi.org/10.1115/1.1504087.
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Rotary viscous couplings with interleaved, perforated plates and viscous fluids are used in automotive systems to transmit torque. During operation, viscous dissipation raises fluid temperature, lowers fluid viscosity and causes the torque transmitted to drop monotonically to unusable levels. Couplings designed with certain plate geometry exhibit a reversal of the torque trend with temperature, and transmit increasingly high torque even under continuous operation. Such couplings achieve torque amplification factors in excess of twenty, compared to earlier couplings. This torque amplification phenomenon has been utilized by industry without fully understanding the mechanisms involved. A comprehensive theory is proposed to explain the complex sequence of events that results in this “anomalous,” but useful phenomenon. Mathematical models are developed for each interdependent process. A visual simulation tool is used to model the intricate dynamics inside the coupling. Results from the simulation model are compared with experimental findings. The various thermodynamic, hydrodynamic, structural and mechanical processes are delineated and tested with a combination of theoretical analysis, computational simulation and experimental observations. The proposed theory identifies, defines and explains the conditions necessary for initiating and sustaining the self-induced torque amplification. The hypotheses are validated by the reasonable agreement of the model with the test results.
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DAŞ, Oğuzhan, and Duygu BAĞCI DAŞ. "İzotropik Plakaların Regressif Topluluk Öğrenmesi Kullanarak Serbest Titreşim Analizi." European Journal of Science and Technology, July 28, 2022. http://dx.doi.org/10.31590/ejosat.1135944.
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The Finite Element Method (FEM) is a popular technique that is employed to analyze and understand the behavior of a structure. Although it has various advantages, there are some drawbacks such as developing accurate mathematical models, the computational cost for complex systems, and expertise. Thanks to recent advancements in computational science, those drawbacks can be eliminated by integrating artificial intelligence. This study presents an ensemble learning regressor-based technique to evaluate the fundamental natural frequencies of isotropic plate structures. For this purpose, Random Forest Regressor (RFR) has been considered. The isotropic plates have been taken into account as square and rectangular thin and thick plates whose materials have been selected as Structural Steel, Aernet 100, Al 7108, and Al 2024 since they are frequently used in various engineering fields. It has been evaluated that the proposed technique has a 0.9936 correlation score (R2) and 0.0019 mean square error (MSE). The average prediction accuracy has been obtained by 99.12% for the test set. Those indicated that the proposed approach is not only an appropriate model for such a problem but also predicts the fundamental natural frequency accurately. Considering its success (99.12%) and the execution speed (0.127 seconds), it is concluded that the proposed approach is an advantageous alternative technique to the other mathematical models.